Anomalous Hall Effect in Ferromagnetic Metals: Role of Phonons at Finite Temperature

Abstract

The anomalous Hall effect in a multiband tight-binding model is numerically studied taking into account both elastic scattering by disorder and inelastic scattering by the electron-phonon interaction. The Hall conductivity is obtained as a function of temperature $T$, inelastic scattering rate $\gamma$, chemical potential $\mu$, and impurity concentration $x_{\mathrm{imp}}$. We find that the new scaling law holds over a wide range of these parameters; $-{\sigma }_{xy}=(\alpha {\sigma }_{xx0}^{-1}+\beta {\sigma }_{xx0}^{-2}){\sigma }_{xx}^2+b$, with ${\sigma }_{\mu \nu }$ (${\sigma }_{\mu \nu 0}$) being the conductivity tensor (with only elastic scattering), which corresponds to the recent experimental observation [Phys. Rev. Lett. {\bf 103} (2009) 087206]. The condition of this scaling is examined. Also, it is found that the intrinsic mechanism depends on temperature under a resonance condition.

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References in corpus (6)

• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Universal Scaling Behavior of Anomalous Hall Effect and Anomalous Nernst Effect in Itinerant Ferromagnets
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Temperature Dependence of the Intrinsic Anomalous Hall Effect in Nickel
• Scattering universality classes of side jump in anomalous Hall effect
• Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

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